"I think we need a very shareholder-oriented shareholder on the board," she said on CNBC's "Fast Money."
Finerman reiterated her call for Apple to put their cash on hand to better use than just sitting on its balance sheet.
Earlier in the day, Greenlight Capital founder David Einhorn appeared on CNBC to argue that Apple needed to find a way to distribute its cash to shareholders.
Finerman proposed the idea of putting Einhorn on Apple's board of directors.
"I'm saying as a shareholder, it's been unbelievably frustrating to have a board that seems to be derelict in their duty of allocating capital," she said.
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"They've done an outstanding, extraordinary job of building a great company. They've done a horrible job of being allocators of capital."